Mistery of Iterators

I'm going crazy for the strange behaviour of the Iterators in Google Apps Script. My script picks a random folder (corresponding to a year between 2012 and the current year), then pick a random image in. The file's random criterion is a led by a random integer which stops the loop at the integer-th iteration. It works, the debug and the script silently execute. But, but, but: the photo-rolling rendering of the script deliveries always the same 4-5 pictures. They are thousands. I control the caching, also the F12 function tabs says the cache is null and Ctrl+F5 does not any positive effect. Then, I ask the script to log the URL of the image. Surprise: even if the random number that enters the if-statement is different, however the resulting URL is the same. By chance, the folder is the same, but the different random numbers get the same image picked. HELP!

function doGet() {
  var folderImmagini_ID ="myID";
  //---
  // picking year folder between 2012 and current year
  var annoCorrente = new Date().getFullYear();
  var numFolderRandom = Math.random() * (annoCorrente - 2011) + 1;
  var nomeFolderRandom = (numFolderRandom + 2011).toString();
  var nomeFolderFinale = nomeFolderRandom.substring(0, nomeFolderRandom.indexOf("."));
  // once get random folder, picking a random image
  var foldersIterator = DriveApp.getFolderById(folderImmagini_ID).getFolders();
  var nomeCartella, cartella;
  while (foldersIterator.hasNext()) {
    cartella = foldersIterator.next(),
    nomeCartella = cartella.getName();
    if (nomeCartella == nomeFolderFinale) {
      var filesIterator = cartella.getFiles();
      var numeroFiles = 0, file;
      while (filesIterator.hasNext()) {
        numeroFiles = numeroFiles + 1;
        file = filesIterator.next();
      }
      var numFileRandom = Math.floor(Math.random() * numeroFiles) + 1;
      var ordineFile = 0;
      filesIterator = cartella.getFiles();
      while (filesIterator.hasNext()) {
        ordineFile = ordineFile + 1;
        if (ordineFile == numFileRandom) {
          var t = HtmlService.createTemplateFromFile('OutputHTML');
          var foto = filesIterator.next();
          t.fotoID = foto.getId();
                         Logger.log("nome folder: %s, numero random: %s, link foto: %s",nomeCartella, numFileRandom, 
                                    "https://drive.google.com/uc?export=download&id="+ t.fotoID);
          return t.evaluate();
        }
      }
    }   
  }
};

<!DOCTYPE html>
<html>
  <head>
    <meta http-equiv="Cache-Control" content="no-cache, no-store, must-revalidate">
    <meta http-equiv="Pragma" content="no-cache">
    <meta http-equiv="Expires" content="0">
  </head>
  <body>
    <center><img src="https://drive.google.com/uc?export=download&id=<?= fotoID ?>" height="85%" width="85%"></center>
  </body>
</html>

Solution

Modification points:

When I saw your showing script, it seems that var foto = filesIterator.next(); is used in the if-statement of if (ordineFile == numFileRandom) {,,,}. In this case, when ordineFile == numFileRandom is true, var foto = filesIterator.next(); is used for the first time. In this case, I'm worried that ordineFile = ordineFile + 1; is not used for selecting the file. I thought that this might be the reason for your current issue.

If you want to modify your showing script, how about the following modification?

From:

while (filesIterator.hasNext()) {
  ordineFile = ordineFile + 1;
  if (ordineFile == numFileRandom) {
    var t = HtmlService.createTemplateFromFile('OutputHTML');
    var foto = filesIterator.next(); // <--- here
    t.fotoID = foto.getId();
    Logger.log("nome folder: %s, numero random: %s, link foto: %s", nomeCartella, numFileRandom,
      "https://drive.google.com/uc?export=download&id=" + t.fotoID);
    return t.evaluate();
  }
}

To:

while (filesIterator.hasNext()) {
  ordineFile = ordineFile + 1;
  var foto = filesIterator.next(); // <--- here
  if (ordineFile == numFileRandom) {
    var t = HtmlService.createTemplateFromFile('OutputHTML');
    t.fotoID = foto.getId();
    Logger.log("nome folder: %s, numero random: %s, link foto: %s", nomeCartella, numFileRandom,
      "https://drive.google.com/uc?export=download&id=" + t.fotoID);
    return t.evaluate();
  }
}

In this case, var foto = filesIterator.next(); was moved outside of the if-statement of if (ordineFile == numFileRandom) {,,,}.

Note:

As another approach, I thought that the file is randomly selected from the file ID list. In this case, how about the following modification?

function doGet() {
  var folderImmagini_ID = "myID";
  //---
  // picking year folder between 2012 and current year
  var annoCorrente = new Date().getFullYear();
  var numFolderRandom = Math.random() * (annoCorrente - 2011) + 1;
  var nomeFolderRandom = (numFolderRandom + 2011).toString();
  var nomeFolderFinale = nomeFolderRandom.substring(0, nomeFolderRandom.indexOf("."));
  // once get random folder, picking a random image
  var foldersIterator = DriveApp.getFolderById(folderImmagini_ID).getFolders();
  var nomeCartella, cartella;

  // I modified the below script.
  while (foldersIterator.hasNext()) {
    cartella = foldersIterator.next(), nomeCartella = cartella.getName();
    if (nomeCartella == nomeFolderFinale) {
      var filesIterator = cartella.getFiles();
      var fileIds = [];
      while (filesIterator.hasNext()) {
        fileIds.push(filesIterator.next().getId());
      }
      var numFileRandom = Math.floor(Math.random() * fileIds.length);
      var t = HtmlService.createTemplateFromFile('OutputHTML');
      t.fotoID = fileIds[numFileRandom];
      Logger.log("nome folder: %s, numero random: %s, link foto: %s", nomeCartella, numFileRandom + 1, "https://drive.google.com/uc?export=download&id=" + t.fotoID);
      return t.evaluate();
    }
  }
}